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@ARTICLE{Park:887788,
      author       = {Park, Gun Woo and Nägele, Gerhard},
      title        = {{M}odeling cross-flow ultrafiltration of permeable particle
                      dispersions},
      journal      = {The journal of chemical physics},
      volume       = {153},
      number       = {20},
      issn         = {0021-9606},
      address      = {Melville, NY},
      publisher    = {American Institute of Physics},
      reportid     = {FZJ-2020-04423},
      pages        = {204110 -},
      year         = {2020},
      abstract     = {Cross-flow ultrafiltration is a pressure-driven separation
                      and enrichment process of small colloidal particles where a
                      colloidal feed dispersion is continuously pumped through a
                      membrane pipe permeable to the solvent only. We present a
                      semi-analytic modified boundary layer approximation (mBLA)
                      method for calculating the inhomogeneous
                      concentration-polarization (CP) layer of particles near the
                      membrane and the dispersion flow in a cross-flow filtration
                      setup with a hollow fiber membrane. Conditions are
                      established for which unwarranted axial flow and permeate
                      flow reversal are excluded, and non-monotonic CP profiles
                      are observed. The permeate flux is linked to the particle
                      concentration on the membrane wall using the
                      Darcy–Starling expression invoking axially varying osmotic
                      and trans-membrane pressures. Results are discussed for
                      dispersions of hard spheres serving as a reference system
                      and for solvent-permeable particles mimicking non-ionic
                      microgels. Accurate analytic expressions are employed for
                      the concentration and solvent permeability dependent
                      dispersion viscosity and gradient diffusion coefficient
                      entering into the effective Stokes flow and
                      advection–diffusion equations. We show that the mBLA
                      concentration and flow profiles are in quantitative
                      agreement with results by a finite element method. The mBLA
                      results are compared with predictions by an earlier CP layer
                      similarity solution, showing the higher precision of the
                      former method.},
      cin          = {IBI-4},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IBI-4-20200312},
      pnm          = {551 - Functional Macromolecules and Complexes (POF3-551) /
                      SFB 985 B06 - Kontinuierliche Trennung und Aufkonzentrierung
                      von Mikrogelen (B06) (221475706)},
      pid          = {G:(DE-HGF)POF3-551 / G:(GEPRIS)221475706},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {33261472},
      UT           = {WOS:000596592100001},
      doi          = {10.1063/5.0020986},
      url          = {https://juser.fz-juelich.de/record/887788},
}